Two conducting concentric, hollow spheres A and B have radii a and b respectively, with A inside B. Their common potentials is V. A is now given some charge such that its potential becomes zero. The potential of B will now be

Options

A. 0
B. `V(1-a//b)`
C. ` Va//b`
D. `Vb//a`

Answer

B

Explanation

They have as common potential in the beginning. This implies that only B has the charge in the beginning.
`:. V=(kq_B)/bor kq_B=Vb`
Now, suppose `q_A` charge is given to A. Then,
`V_A=(kq_A)/a+(kq_B)/b=0`
or `kq_A=-a((kq_B)/b)=-aV`
Now, `V_B=(kq_A)/b+(kq_B)/b`
`=-a/bV+V=V(1-a/b)`